Difference between revisions of "User:Tohline/Math/EQ PplusHalf01"
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(Created page with '<table border="0" cellpadding="5" align="center"> <tr> <td align="right"> [[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templat…') |
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[[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templates# | [[Image:LSU_Key.png|25px|link=http://www.vistrails.org/index.php/User:Tohline/Appendix/Equation_templates#Toroidal_Function_Evaluations]] | ||
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<math>~P_{+ 1 | <math>~P_{+ \frac{1}{2}}(z)</math> | ||
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<math>~P_{+1 | <math>~P_{+ \frac{1}{2}}(\cosh\eta)</math> | ||
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[https://books.google.com/books?id=MtU8uP7XMvoC&printsec=frontcover&dq=Abramowitz+and+stegun&hl=en&sa=X&ved=0ahUKEwialra5xNbaAhWKna0KHcLAASAQ6AEILDAA#v=onepage&q=Abramowitz%20and%20stegun&f=false Abramowitz & Stegun (1995)], p. | [https://books.google.com/books?id=MtU8uP7XMvoC&printsec=frontcover&dq=Abramowitz+and+stegun&hl=en&sa=X&ved=0ahUKEwialra5xNbaAhWKna0KHcLAASAQ6AEILDAA#v=onepage&q=Abramowitz%20and%20stegun&f=false Abramowitz & Stegun (1995)], p. 337, eq. (8.13.5) | ||
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<td align="center" colspan="3"> | <td align="center" colspan="3"> | ||
[https://books.google.com/books?id=MtU8uP7XMvoC&printsec=frontcover&dq=Abramowitz+and+stegun&hl=en&sa=X&ved=0ahUKEwialra5xNbaAhWKna0KHcLAASAQ6AEILDAA#v=onepage&q=Abramowitz%20and%20stegun&f=false Abramowitz & Stegun (1995)], p. | [https://books.google.com/books?id=MtU8uP7XMvoC&printsec=frontcover&dq=Abramowitz+and+stegun&hl=en&sa=X&ved=0ahUKEwialra5xNbaAhWKna0KHcLAASAQ6AEILDAA#v=onepage&q=Abramowitz%20and%20stegun&f=false Abramowitz & Stegun (1995)], p. 337, eq. (8.13.6) | ||
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Latest revision as of 21:42, 1 July 2018
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<math>~P_{+ \frac{1}{2}}(z)</math> |
<math>~=</math> |
<math>~ \frac{2}{\pi} \biggl[z + \sqrt{ z^2-1} \biggr]^{1 / 2} ~E\biggl( \sqrt{ \frac{2(z^2-1)^{1 / 2}}{z + (z^2-1)^{1 / 2}}} \biggr) </math> |
for example … |
<math>~P_{+ \frac{1}{2}}(\cosh\eta)</math> |
<math>~=</math> |
<math>~ \frac{2}{\pi}~e^{\eta/2}~ E( \sqrt{1-e^{-2\eta}} ) </math> |
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Abramowitz & Stegun (1995), p. 337, eq. (8.13.5) |
Abramowitz & Stegun (1995), p. 337, eq. (8.13.6) |
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